Needing two runs off the last ball of the match, skipper Mahendra Singh Dhoni clipped Stuart Binny off his pads to help the Super Kings overhaul the target of 147 set by Rajasthan.
Du Plessis was the main scorer as he smashed six fours and two sixes to set the tone for the defending champions at the MA Chidambaram Stadium.
This was the Super Kings' fourth win from seven matches while Rajasthan, who had four wins prior to this match, suffered their third defeat in this edition of the cash-rich Twenty20 league.
Chasing a rather modest total, the Super Kings were off to a sedate start, by IPL's standards, as openers du Plessis and Subramaniam Badrinath (15) added 55 runs in eight overs.
Slow left-arm spinner Brad Hogg gave the visitors their first breakthrough when he had Badrinath stumped by Shreevats Goswami with a ball that had a bit of flight.
The dismissal, though, hardly had any effect on du Plessis as he continued with his attacking game and, along with Suresh Raina, added 61 runs for the second wicket, much to delight of the home crowd.
Image: Chennai Super Kings batsman Francois Du Plessis hits a six during the IPL Twenty20 cricket match between Chennai Super Kings and Rajasthan Royals at The M.A.Chidambaram Stadium in Chennai on April 21, 2012.